The document outlines the properties and characteristics of parallelograms and rectangles, enabling students to prove and apply these properties in problem-solving. It specifies that parallelograms have opposite sides and angles that are congruent, with supplementary consecutive angles, and diagonals that bisect each other. Rectangles inherit these properties from parallelograms, with the additional feature that their diagonals are congruent.

1. 2.7.2 Parallelograms & Rectangles
The student is able to (I can):
• Prove and apply properties of parallelograms.
• Use properties of parallelograms to solve problems.
• Prove and apply properties of rectangles.
• Use properties of rectangles.

2. parallelogram
Properties of
Parallelograms
A quadrilateral with two pairs of parallel
sides.
Therefore, if a quadrilateral is a
parallelogram, then it has two pairs of
parallel sides.
>>
>>
T I
ME
TI ME, TE IM

3. Properties of
Parallelograms
If a quadrilateral is a parallelogram, then
opposite sides are congruent.
If a quadrilateral is a parallelogram, then
opposite angles are congruent.
KI NG, GK IN≅ ≅
K
NG
I
>>
>>
K
NG
O
∠K ≅ ∠N, ∠O ≅ ∠G

4. Properties of
Parallelograms
If a quadrilateral is a parallelogram, then
consecutive angles are supplementary.
If a quadrilateral is a parallelogram, then
its diagonals bisect each other.
1 2
34
m∠1 + m∠2 = 180°
m∠2 + m∠3 = 180°
m∠3 + m∠4 = 180°
m∠4 + m∠1 = 180°
>>
>>
T U
NE
SSSS
TS NS,ES US≅ ≅

5. Examples Find the value of the variable:
1. x =
2. x =
3. y =
5x + 3 2x + 15
4
(3x)º
(x + 84)º
yº
5x + 3 = 2x + 15
3x = 12
3x = x + 84
2x = 84
42
3(42) = 126º
y = 180 — 126
54

6. rectangle A parallelogram with four right angles.
If a parallelogram is a rectangle, then its
diagonals are congruent (“checking for
square”).
F I
SH
≅FS IH

7. Because a rectangle is a parallelogram, it
also “inherits” all of the properties of a
parallelogram:
• Opposite sides parallel
• Opposite sides congruent
• Opposite angles congruent (actually allallallall
angles are congruent)
• Consecutive angles supplementary
• Diagonals bisect each other

8. Example Find each length.
1. LW
LW = FO = 30
2. OL
OL = FW = 2(17) = 34
3. OW
∆OWL is a right triangle, so
OW = 16
F O
WL
30
17
+ =2 2 2
OW LW OL
+ =2
OW 900 1156
=2
OW 256
+ =2 2 2
OW 30 34